Momentum is conserved, so the sum of the momenta of the bullet and block before collision is equal to the momentum of the combined bullet-block system,
[tex]m_bv_b+m_wv_w = (m_b+m_w)v[/tex]
where v is the speed of the bullet-block system. The block starts at rest so it has no initial momentum, and solving for v gives
[tex]v = \dfrac{m_b}{m_b+m_w} v_b[/tex]
The total work W performed by the spring on the bullet-block system as it is compressed a distance x is
[tex]W = -\dfrac12kx^2[/tex]
where k is the spring constant, and the work done is negative because the restoring force of the spring opposes the bullet-block as it compresses the spring.
By the work-energy theorem, the total work done is equal to the change in the bullet-block's kinetic energy ∆K, so we have
[tex]W_{\rm total} = W = \Delta K[/tex]
The bullet-block starts moving with velocity v found earlier and comes to a stop as the spring slows it down, so we have
[tex]-\dfrac12kx^2 = -\dfrac12(m_b+m_w)v^2 \implies kx^2 = \dfrac{{m_b}^2}{m_b+m_w}{v_b}^2[/tex]
Solve for [tex]m_w[/tex]:
[tex]m_w=\dfrac1k\left(\dfrac{m_bv_b}x\right)^2-m_b[/tex]
[tex]m_w=\dfrac1{205\frac{\rm N}{\rm m}}\left(\dfrac{(0.0135\,\mathrm{kg})\left(245\frac{\rm m}{\rm s}\right)}{0.350\,\rm m}\right)^2-0.0135\,\mathrm{kg}\approx \boxed{0.422\,\mathrm{kg}}[/tex]
Group elements number 11 to 20 as either metallic, non metallic or metalloid.
Answer:
The elements are grouped into the different substances by color. As you can see, Lithium, Beryllium, Sodium, Magnesium, Aluminum, Potassium, and Calcium are metals out of the first 20 elements.
Hydrogen, Helium, Carbon, Nitrogen, Oxygen, Fluorine, Neon, Phosphorus, Sulfur, Chlorine, and Argon, are non-metals within the first 20 elements.
Boron and Silicon count as Metalloids in the Periodic Table (properties of both metals and non-metals)
reference- socatric q and a
Explanation:
Answer:
(11-13) - Metals
(14) - Metalloid
(15-18) - Non- metals
(19-20) - Metals
Explanation:
The elements from 11 to 13 are metals. They are Sodium(Na), Magnesium(Mg) and Aluminum(Al) respectively.
The element 14 is a metalloid. It’s Silicon(Si).
The elements from 15 to 18 are non metals. The 18th element is a noble gas known as Argon(Ar).
The elements from 15 to 17 are Phosphorus(P), Sulphur(S) and Chlorine(Cl).
The elements from 19 to 20 are metals. They are Potassium(K) and Calcium(Ca).
Which type of electromagnetic wave is deliberately used in some
circumstances to cause damage to living cells in the human body?
A. Infra-red
B. Gamma rays
C. Microwaves
D. Radio waves.
Gamma rays
used in radiotherapy
why is it important to have regular super vision of the weights and the measurements in the market?
Answer:
Obeying to weights & measurement regulations in both national and international metrology legislation, standards and test procedures is a requirement to participate in any market because it's aimed to safeguard the consumers and promote fair competition, which provides efficiency and saves unnecessary costs to U.S. businesses and stakeholders.
Explanation:
In the U.S., the National Institute of Standards and Technology (NIST) has an Office of Weights and Measures (OWM) that represents the country in the International Organization of Legal Metrology (OIML)
Two stones are dropped from the edge of a 60m cliff , the second stone 1.6secon after the first . How far below the top of the cliff is the second stone when the separation between the two stone is 36m?
Answer:
The separation between the two stones is 36 m, when the second stone is approximately 10.9 m below the top of the cliff
Explanation:
The given parameters are;
The height of the cliff from which the stones are dropped, h = 60 m
The time at which the second stone is dropped = 1.6 seconds after the first
The distance below the top of the cliff when the distance between the two stones is 36 m = Required
We have;
The kinematic equation of motion that can be used is s = u·t - (1/2)·g·t²
For the first stone, we have, s₁ = u·t₁ - (1/2)·g·t₁²
For the second stone, we get; s₂ = u·t₂ - (1/2)·g·t₂²
t₁ = t₂ + 1.6
g = The acceleration due to gravity ≈ 9.81 m/s²
s = The distance below the cliff top
The initial velocity of the stones, u = 0
Let t represent the time from which the second stone is dropped at which the distance between the two stones is 36 m, we have;
s₁ = u·(t + 1.6) + (1/2)·g·(t + 1.6)²
s₂ = u·t + (1/2)·g·t²
u = 0
∴ s₁ - s₂ = 36 = (1/2)·g·(t + 1.6)² - (1/2)·g·t²
2 × 36/(g) = (t + 1.6)² - t² = t² + 3.2·t + 2.56 - t² = 3.2·t + 2.56
2 × 36/(9.81) = 3.2·t + 2.56
t = (2 × 36/(9.81) - 2.56)/3.2 = ≈ 1.49 s
t ≈ 1.49 s
s₂ = (1/2)·g·t²
∴ s₂ = (1/2) × 9.81 × 1.49² ≈ 10.9
The distance below the top of the cliff of the second stone when the the separation between the two stones is 36 m, s₂ ≈ 10.9 m.
In a Rutherford scattering experiment, alpha parti- cles having kinetic energy of 7.70 MeV are fired toward a gold nucleus that remains at rest during the collision. The alpha particles come as close as 29.5 fm to the gold nucleus before turning around. (a) Calculate the de Broglie wave- length for the 7.70-MeV alpha particle and compare it with the distance of closest approach, 29.5 fm. (b) Based on this comparison, why is it proper to treat the alpha particle as a particle and not as a wave in the Rutherford scattering experiment
(a) The de Broglie wavelength is approximately 5.175 × 10⁻¹⁵ meters. The wavelength is lesser than the distance of closest approach
(b) It is proper to treat the alpha particle as a particle and not as wave because the distance of closest approach is much larger than and not comparable to its wavelength for the alpha particle for the alpha particle to be treated as a wave
The given parameters are;
The kinetic energy of the alpha particles = 7.70 MeV = 1.23368 × 10⁻¹² J
The distance from the gold nucleus the alpha particles reach = 29.5 fm
(a) The de Broglie wavelength of a particle is given as follows;
[tex]\mathbf{\lambda = \dfrac{h}{p}}[/tex]
Where;
λ = The wavelength
h = Planck's constant = 6.62607004 × 10⁻³⁴ m²·kg/s
p = The momentum of the particle = Mass of an electron, m × Velocity, v
The mass of an alpha particle, m ≈ 6.645 × 10⁻²⁷ kg
Therefore;
[tex]\lambda = \dfrac{h}{m \times v}[/tex]
The kinetic energy of the alpha particle, K.E. = (1/2)·m·v²
∴ v = √(2 × K.E./m)
Therefore;
[tex]\lambda = \dfrac{h}{m \times \sqrt{2 \times \dfrac{K.E.}{m} } } = \dfrac{h}{ \sqrt{2 \times m \times K.E.} }[/tex]
Plugging in the values of the variables gives;
[tex]\lambda = \dfrac{6.62607004 \times 10 ^{-34} }{ \sqrt{2 \times 6.645 \times 10 ^{-27} \times 1.23368 \times 10^{-12} } } \approx 5.175 \times 10^{-15}[/tex]
The de Broglie wavelength of the alpha particle, λ ≈ 5.175 × 10⁻¹⁵ m
The distance of closest approach = 29.5 fm = 29.5 × 10⁻¹⁵ m
Compared to the distance of closest approach, the wavelength of the alpha particle is lesser than the distance of closest approach
(b) Given that the distance of closest approach is six times larger than the wavelength of the alpha particle, and alpha particle behaving as waves are expected to approach closer to the gold nucleus in the region of their wavelength before deflection, therefore, the larger distance of closest approach is indicative of a charged particle to charged particle interaction, and therefore, particle behavior of alpha particles.
Learn more about de Broglie wavelength, particles and wave behavior of radiation here;
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Which are characteristics of a prokaryotic cell? Select three options.
O contains DNA
O lacks DNA
O contains ribosomes
O lacks ribosomes
O contains a nucleus
O lacks a nucleus
I NEED THIS QUICKLY
Answer:
A. Contains DNA
C. Contains ribosomes
F. Lacks a nucleus
Explanation:
An aluminium block of mass 1 kg is heated by an electric heater for 3 minutes and a temperature rise of 15 °C is recorded. If the electric heater is connected to a voltmeter which gives a reading of 30 V and an ammeter which gives a reading of 2.5 A, calculate the specific heat capacity of the aluminium.
Answer:
the specific heat capa city of the aluminium is 900 joules per kilogram per °C.
Am I right please?
Which of the following can be correct units for acceleration?
A. miles/hr/m
B. Km/s/hr
C. m/s/m
D. km/m/s
Answer:
B. Km/s/hr
Explanation:
sort out electric current as fundamental or derived unit.
Answer:
electric current is derived unit.
Explanation:
According to the definition of electric current, it appears to be a derived quantity. Charge on the other hand seems more fundamental than electric current.
Q- Wheel of a running vehicle has which energy?
(a) Vibrational Kinetic energy
(b) Translational Kinetic energy
(c) Rotational Kinetic energy
(d) All of the above
Answer:
Rotational kinetic energy
Explanation:
It is caused by circular motion.
e. write unit of the following physical quantities
Answer:
electric current=ampere(A)
force=Newton (N)
area=metres square(m^2)
power=watt(w)
density=kg/m3
amount of substance =mole per cubic meter (mol/m3).
volume=cubic meter (m3),
Answer:
thanks for brainlist brother.........
Un muelle se alarga 20 cm cuando ejercemos sobre él una fuerza de 24 N. Calcula:El valor de la constante elástica del muelle
Answer:
120 Nm-1
Explanation:
Según la ley de Hooke;
F = Ke
F = fuerza sobre el resorte
K = constante de fuerza
e = extensión
Por eso;
K = F / e
K = 24N / 20 × 10 ^ -2m
K = 120 Nm-1
What would be the acceleration in a body moving with uniform velocity and why?
Explanation:
The derivative of a constant term is always 0. So the acceleration of the body would be zero. Hence, the acceleration of a body moving with uniform velocity will always be zero.
hope it helps you
Make a tree diagram based on the topic motion which includes all the concept like uniform & non uniform motion accelerated motion equation of motion motion etc
I think it is a education tips
Why are road accidents at high speeds very much worse than road accidents at low speeds?
Answer:
The momentum makes it worse.
Explanation:
The momentum of vehicles running at faster speeds is very high and causes a lot of damage to the vehicles.
20. A semiconductor is a
crystalline solid that conducts current under any condition
metallic solid that conducts current under any condition
metallic solid that conducts current under certain conditions
crystalline solid that conducts current under certain conditions
Answer:
D. crystalline solid that conducts current under certain conditions
Explanation:
Semiconductors are crystalline solids that has the ability to conduct electrical currents but on certain conditions e.g heat. The conduction of semiconductors is less than that of conductors (metals) but more than insulators (nonmetals), hence, they are said to be intermediates of conductors and insulators in terms of electrical conductivity.
Examples of semiconductors are silicon, boron, carbon, germanium, arsenic etc.
Một con lắc lò xo gồm 1 quả nặng có m= 0,2kg treo vào lò xo có độ cứng k= 100N/m, cho vật dao động điều hoà theo phương thẳng đứng với biên độ A= 1,5 cm. Lực đàn hồi cực đại có giá trị
how can we maintain peace in the nature and surrounding
Answer:
6 Ways To Promote Peace
Treat all people with kindness, regardless of race, gender orientation, sexual orientation, religion, etc.
Attend a peace rally.
Write to your government (local and federal)
Create a peaceful affirmation/mantra.
Don't engage in violence of any kind.
Don't purchase weapons.
Can acceleration and velocity be equal vectors?
Answer:
Velocity is the rate of change of position with respect to time, whereas acceleration is the rate of change of velocity. Both are vector quantities (and so also have a specified direction), but the units of velocity are meters per second while the units of acceleration are meters per second squared.
Un auto se desplaza por una carretera recta a una velocidad de 85 km/h. Al cabo de 2 horas, ¿qué distancia habrá recorrido, en metros?
Answer:
Distancia, D = 170,000 metros
Explanation:
Dados los siguientes datos;
Velocidad = 85 km/h Tiempo = 2 horasPara encontrar la distancia recorrida, en metros;
Matemáticamente, la distancia recorrida por un objeto se calcula mediante la fórmula;
Distancia = velocidad * tiempo
Sustituyendo los valores en la fórmula, tenemos;
Distancia = 85 * 2
Distancia = 170 kilómetros
A continuación, convertiríamos el valor en kilómetros a metros;
Conversión:
1 kilómetros = 1000 metros
170 kilómetros = D metros
Multiplicación cruzada, tenemos;
D = 170 * 1000
D = 170,000 metros
Por lo tanto, habría viajado 170,000 metros después de 2 horas.
Question 3 of 10
Which image shows an example of the strong nuclear force in
action?
A.
B.
C.
D.
Answer: The answer is B
Explanation:
There are 4 fundamental forces that hold matter together.
- Gravitational Force
- Electromagnetic Force
- Strong Nuclear Force
- Weak Nuclear Force
We have barely just scratched the info about nuclear forces but the reason why B is the answer to the question is that Strong nuclear force actually holds the protons and neutrons together in the nucleus of an atom, much like the picture in B.
Answer: B
Explanation:
3 An un calibrated mercury in glass thermometer immersed in melting ice. The length of the mercury thread is 25 mm when the thermometer immersed in steam from pure water boiling under a pressure of 1 atmosphere the length of the thread is 200 mm what is the temperature in degree centigrade when the length of the thread is 95mm.
Answer:
25 mm = 0 deg C
200 mm = 100 deg C
200 - 25 = 175 = change in thread per 100 deg C
95 - 25 = 70 mm - change in thread from 0 deg C
70 / 175 * 100 = 40 deg C final temperature at 95 mm
Write the dimension of a / b in the x = at + bt2. Where x is the distance and t is the time?
The dimension of a/b where x is the distance and t is the time is T
Given the expression
x = at + bt²
where
x is the distance
t is the time
Based on the homogeneity principle, the expression on the left-hand side must be equal to that on the right. Hence;
x = at
[tex]a = \frac{x}{t}[/tex]
Since x is the distance and distance is measured in metres, the dimension equivalent will be the length 'L'
Since t is the time and time is measured in seconds, the dimension equivalent will be the seconds 'T'
[tex]a=\frac{L}{T}[/tex]
Similarly;
x = bt²
[tex]b=\frac{x}{t^2}\\b=\frac{L}{T^2}[/tex]
Next is to get a/b;
[tex]\frac{a}{b} = \frac{L}{T} \div \frac{L}{T^2}\\\frac{a}{b} = \frac{L}{T}*\frac{T^2}{L} \\\frac{a}{b} =\frac{T^2}{T}\\\frac{a}{b} =T[/tex]
Hence the dimension of a/b is T
the force between the earth and the body which is at a distance r from the center of the earth is F. What must be this distance for the force to be doubled.
Answer:
Explanation:
The gravitational force between the earth and another body is F = -GM_em/r^2 r where G = 6.67 times 10^-11 Nm^2/kg^2 is the gravitational constant, M_e = 5.97 times 10^24 kg is the mass of the earth, m is the mass of the other body, and r is the position vector of the second body with respect to the centre of the earth.
solve two questions under inclined plane using Newton 2nd law
Explanation:
If the mass of the inclined plane is large enough, could N ever be equal to mgcosθ. Reasons?
So far I've come up with: mgcosθ−N=ma meaning if N were to equal mgcosθ, ma=0. Since the surfaces are frictionless and since N is acting on the inclined plane too(it'll have a horizontal component), this isn't possible. Am I right? Where am I going wrong?
84. Three resitors each of value 30 respectively are connected in a parallel
combination across a 10 V battery the current through each resitor is
Answer:
each resistor draws 1/3 of an amp or 0.33333 amps
Explanation:
V = I * R
V = 10 volts
R = 30 ohms
10 = I * 30 Divide by 30
10/30 = I
I = 0.33333
For problems 2-3, a Ferrari accelerates from 0-60.0 miles per hour in 2.50 seconds.
2. What is its final speed, in m/s?
a 5.6 m/s
b. 13 m/s
c. 26.8 m/s
d. 1608 m/s
0-60.0 per near
2.50 seconds
3. What is its average acceleration?
a. 24.0 m/s
b. 10.7 m/s2
c. 38.6 m/s2
d. 13 m/s
Answer:
Explanation:
The first part of this question is simply asking us to convert the speed from miles per hour to meters per second:
[tex]60.0\frac{mi}{hr}*\frac{1hr}{3600sec}*\frac{1609.34m}{1mi}=26.8\frac{m}{s}[/tex] choice C.
The next part wants us to use the equation for acceleration and find the acceleration:
[tex]a=\frac{v-v_0}{t}[/tex] where v is final velocity, v0 is initial velocity, and t is time in seconds (which was one of the reasons we had to convert the initial velocity from 60.0 mph to m/s):
[tex]a=\frac{26.8-0}{2.5}[/tex] and
a = 10.7 m/s/s, choice B.
Si dejamos caer un objeto desde una gran altura, ¿será que tiene siempre la misma velocidad
Answer:
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can anyone help me with this one
Answer:
c) sin c /sin d
because light is moving from denser to shallower medium
b) refraction of light
Explanation:
What is the decay constant for Oxygen-19 if it has a half-life of 26.5s?
A)0.0262/s
B)18.4
C)0.0377/s
C)38.2/s
Answer:
Option A.
Explanation:
We define the half time T as the time such that an initial quantity A reduces to its half.
So we can model the quantity as a function of time like:
P(t) = A*e^(-k*t)
Then for the half time, T, we will have:
P(T) = A/2 = A*e^(-k*T)
solving for k, we get:
A/2 = A*e^(-k*T)
1/2 = e^(-k*T)
ln(1/2) = ln( e^(-k*T)) = -k*T
-ln(1/2)/T = k
Here we know that the half time is T = 26.5s
if we input that in the above equation, we get:
-ln(1/2)/26.5s = k = 0.0262 s^-1
Then the correct option is A
